Interacting Bose and Fermi gases in low dimensions and the Riemann hypothesis

We apply the S-matrix based finite temperature formalism to non-relativistic Bose and Fermi gases in 1+1 and 2+1 dimensions. In the 2+1 dimensional case, the free energy is given in terms of Roger's dilogarithm in a way analagous to the relativistic 1+1 dimensional case. The 1d fermionic case with a quasi-periodic 2-body potential provides a physical framework for understanding the Riemann hypothesis.Comment: version 3: additional appendix explains how the $\nu$ to $1-\nu$ duality of Riemann's $\zeta (\nu)$ follows from a special modular transformation in a massless relativistic theor

Designing institutional multi-agent systems

The vision of agents working together on the Internet, in virtual organizations, is one that is increasingly common. However, one of the issues is the regulation of the participating agents and their behaviour. A substantial body of work exists that investigates agent societies and agent organizations, including work on electronic institutions, such as Islander and Ameli. However, although such work provides concrete tools for specifying and enacting institutions, there is a lack of clear documented guidance to designers who are using these tools. In this paper we describe a methodology for developing an institutional structure for multi agent systems. This methodology captures the knowledge and experience within the Islander group, and integrates it with the Prometheus methodology. This work was supported by the Australian Research Council under grant LP0453486, in collaboration with Agent Oriented Software. We also thank the Australian Tourism Data Warehouse for use of their tourism content in our agents. Carles Sierra is being supported by the Spanish Web-I(2) project and the ARC Discovery Grant DP0557168

The elementary excitations of the exactly solvable Russian doll BCS model of superconductivity

The recently proposed Russian doll BCS model provides a simple example of a many body system whose renormalization group analysis reveals the existence of limit cycles in the running coupling constants of the model. The model was first studied using RG, mean field and numerical methods showing the Russian doll scaling of the spectrum, E(n) ~ E0 exp(-l n}, where l is the RG period. In this paper we use the recently discovered exact solution of this model to study the low energy spectrum. We find that, in addition to the standard quasiparticles, the electrons can bind into Cooper pairs that are different from those forming the condensate and with higher energy. These excited Cooper pairs can be described by a quantum number Q which appears in the Bethe ansatz equation and has a RG interpretation.Comment: 36 pages, 12 figure

Spin precession and spin Hall effect in monolayer graphene/Pt nanostructures

Spin Hall effects have surged as promising phenomena for spin logics operations without ferromagnets. However, the magnitude of the detected electric signals at room temperature in metallic systems has been so far underwhelming. Here, we demonstrate a two-order of magnitude enhancement of the signal in monolayer graphene/Pt devices when compared to their fully metallic counterparts. The enhancement stems in part from efficient spin injection and the large resistivity of graphene but we also observe 100% spin absorption in Pt and find an unusually large effective spin Hall angle of up to 0.15. The large spin-to-charge conversion allows us to characterise spin precession in graphene under the presence of a magnetic field. Furthermore, by developing an analytical model based on the 1D diffusive spin-transport, we demonstrate that the effective spin-relaxation time in graphene can be accurately determined using the (inverse) spin Hall effect as a means of detection. This is a necessary step to gather full understanding of the consequences of spin absorption in spin Hall devices, which is known to suppress effective spin lifetimes in both metallic and graphene systems.Comment: 14 pages, 6 figures. Accepted in 2D Materials. https://doi.org/10.1088/2053-1583/aa882

Dualities in Spin Ladders

We introduce a set of discrete modular transformations $T_\ell,U_\ell$ and $S_\ell$ in order to study the relationships between the different phases of the Heisenberg ladders obtained with all possible exchange coupling constants. For the 2 legged ladder we show that the $RVB$ phase is invariant under the $S_\ell$ transformation, while the Haldane phase is invariant under $U_\ell$. These two phases are related by $T_\ell$. Moreover there is a "mixed" phase, that is invariant under $T_\ell$, and which under $U_\ell$ becomes the RVB phase, while under $S_\ell$ becomes the Haldane phase. For odd ladders there exists only the $T_\ell$ transformation which, for strong coupling, maps the effective antiferromagnetic spin 1/2 chain into the spin 3/2 chain.Comment: REVTEX file, 5 pages, 2 EPS figure

Did the Student Engage in Academic Dishonesty on their Exam? Yes, No, and Shades of Grey in Decision Making

In academia, there are guidelines as to what constitutes academic dishonesty, and how to report it. This leads to the assumption that when instances arise, there are clear yes or no answers to the questions: (a) did the student engage in academic dishonesty, and (b) how should the student be disciplined? Previous research has been conducted examining the behaviours students engage in and the repercussions, but less research has examined the cognitions and actions of the people who discover the instances of academic dishonesty. Therefore, the purpose of this study was to examine how participants make sense of potential academic dishonesty scenarios and the resulting actions they would take. We presented 201 preservice teachers with three scenarios: (a) sneaking answers into an exam, (b) having someone tell you the answers and (c) peeking at someone else’s answers. For each scenario, they had to respond to the items (1) to what extent do you consider the student’s behaviour as academic dishonesty, (2) What in the story helped you decide on your response? and (3) What do you think is an appropriate form of discipline? Overall, participants strongly agreed the behaviours were academically dishonest, however, when asked to indicate what in the story helped them decide, the majority made embellishments to the story, and close to half of the participants provided their opinions related to academic dishonesty more broadly. Moreover, participants indicated a wide range of disciplines for the same scenarios. The results will be utilized to create discussion around decision-making and academic dishonesty

Teaching Statistics for Social Justice - An Autoethnographic Research Report

The following autoethnography was completed by two graduate students at University A learning to enact teaching for social justice while building content underpinnings in statistics at University B. The authors present a research base for teaching for social justice followed by a description of their lesson, observations during enactment, and reflection of change in beliefs about teaching for social justice afterward. Findings in this study are shared from the authors’ personal perspectives through the enactment of teaching a lesson for social justice in an undergraduate statistics course at University B. Implications provide encouragement that the inclusion of social justice topics in undergraduate and graduate level teacher educator coursework may improve teacher attention to equity in practice

Algebraic Bethe Ansatz for a discrete-state BCS pairing model

We show in detail how Richardson's exact solution of a discrete-state BCS (DBCS) model can be recovered as a special case of an algebraic Bethe Ansatz solution of the inhomogeneous XXX vertex model with twisted boundary conditions: by implementing the twist using Sklyanin's K-matrix construction and taking the quasiclassical limit, one obtains a complete set of conserved quantities, H_i, from which the DBCS Hamiltonian can be constructed as a second order polynomial. The eigenvalues and eigenstates of the H_i (which reduce to the Gaudin Hamiltonians in the limit of infinitely strong coupling) are exactly known in terms of a set of parameters determined by a set of on-shell Bethe Ansatz equations, which reproduce Richardson's equations for these parameters. We thus clarify that the integrability of the DBCS model is a special case of the integrability of the twisted inhomogeneous XXX vertex model. Furthermore, by considering the twisted inhomogeneous XXZ model and/or choosing a generic polynomial of the H_i as Hamiltonian, more general exactly solvable models can be constructed. -- To make the paper accessible to readers that are not Bethe Ansatz experts, the introductory sections include a self-contained review of those of its feature which are needed here.Comment: 17 pages, 5 figures, submitted to Phys. Rev.